Mass flow measuring apparatus utilizing the effect of Coriolis force are based on the physical phenomenon, that Coriolis force acts on a conduit if it is vibrated perpendicular to the direction of flow through the conduit. The magnitude of the Coriolis force depends on the angular velocity of the vibration and the mass flow. The Coriolis force is a periodic force with a frequency equal to the frequency of vibration. As a consequence, a phase difference (time lag) in motion is obtained if a conduit fixed at two points is vibrated at its centre between the two supports and the motion is measured by sensing devices at two points located symmetrically at both sides of the centre, which results from the superposition of the vibrating force and the Coriolis force and is proportional to the mass flow. Signal processing units of mass flow meters calculate the mass flow on the basis of signals of sensing devices located symmetrically. The design and operating characteristics of Coriolis mass flow meters; are closely related to the conduit assembly used.
The mass flow information is always carried by the component caused by the Coriolis force in the electric signal supplied by the sensing devices that are located symmetrically to the centre of the conduit. The signal processing units measure either this specific component or another parameter traceable to this. Such parameters are e.g. time lag between the two signals, the integral formed from the absolute values of signal differences for a finite number of full periods etc.
Signal processing units of this kind are described in British Patent No. 2,171,200, U.S. Pat. No. 4,879,911, Hungarian Patent No. 200,234, International Patent Application No. WO 88/03261 and U.S. Pat. Nos. 4,655,089 and 4,996,871.
The apparatus described in the British Patent No. 2,171,200 is connected to a conduit assembly having a pair of straight conduits parallel to each other. The effect of the interfering longitudinal (axial) stresses generated during the vibration of the straight conduit sections are eliminated by generating the vibration at the fundamental resonant frequency and its third harmonic frequency simultaneously, while utilizing the property of the pair of parallel conduits that the ratio of the fundamental frequency to its third harmonic carries information about the axial stresses. In a first approach, the mass flow will be determined on the basis of the phase difference obtained at the fundamental frequency and, then, the result thus obtained will be corrected taking the measured ratio of the fundamental frequency to its third harmonic into account.
The apparatus described in U.S. Pat. No. 4,879,911 reduces the measuring task to the measurement of time difference. By analog integration of the signals of the sensing devices a reference signal and a measuring signal proportional to the displacement will be obtained. By comparing these signals with zero-symmetric reference voltages, gate-times are obtained, that contain the time lag between the signals with various signs. By summing the gate times with proper signs, the time lag between the signals will be obtained, which is proportional to the mass flow.
The apparatus described in Hungarian Patent No. 200,234 uses the integral value of the signals of the sensing devices to calculate the mass flow.
By adding the frequency component associated with the deformation caused by the Coriolis force to the driving signal, the effect of Coriolis force will be significantly increased. This is utilized by the apparatus described in International Patent Application No. WO 88/03261, in which four independent driving and sensing elements are used. The signal caused by the Coriolis force and the driving signal, contained in the complex input signals, are separated by means of synchronous rectifiers and the mass flow is calculated on the basis of the ratio of these two component signals.
The apparatus described in U.S. Pat. No. 4,655,089 uses an integrator with coupled capacitors to generate signals proportional to the displacement. The signals thus obtained will be fed to a voltage comparator each of variable reference, which control a phase comparator. The phase comparator sets the output voltages of digital-analog converters through a digital counter so as to obtain zero (or constant) time delay at the input of the phase comparator while using the said output voltages as references to the said voltage comparators. In the equilibrium once obtained, the difference between the control codes of digital-analog converters will be proportional to the mass flow.
In U.S. Pat. No. 4,996,871 a Coriolis densimeter is described which relies on measuring mass flow rate by determining the phase difference that occurs between real and imaginary components of the discrete Fourier transformation of signals of two velocity sensors attached to the conduits vibrated. The analog signals of the sensors are multiplexed, filtered with an anti-aliasing low pass filter, then subject to a sample and hold function and digitalized in order to performe the discrete Fourier transformation. Alternatively, a separate low pass filter could be situated in front of the multiplexer for each of the two incoming velocity signals in lieu of the anti-aliasing filter. Unfortunately, the use of such filters may result in measurements error as their characteristics vary due to temperature variations and thereby influencing the phases of the signal to be measured. Moreover, in the apparatus described the samples of the two signals are interleaved, i.e. they cannot be sampled at the same time. This phase shift has to be compensated which is rather complicated and represents a further source of measurement error.